The member experiences the end moments M AB and M BA at A and B, respectively, and undergoes the deformed shape shown in Figure 11.1b, with the assumption that the right end B of the member settles by an amount ∆. To derive the slope-deflection equations, consider a beam of length L and of constant flexural rigidity EI loaded as shown in Figure 11.1a. The rotation of the chord connecting the ends of a member ( ), the displacement of one end of a member relative to the other, is positive if the member turns in a clockwise direction.ġ1.3 Derivation of Slope-Deflection Equations The rotation θ of a joint is positive if its tangent turns in a clockwise direction. For the determination of the end moments of members at the joint, this method requires the solution of simultaneous equations consisting of rotations, joint displacements, stiffness, and lengths of members.Īn end moment M is considered positive if it tends to rotate the member clockwise and negative if it tends to rotate the member counter-clockwise.

Thus, the unknowns in the slope-deflection method of analysis are the rotations and the relative joint displacements. The method accounts for flexural deformations, but ignores axial and shear deformations. Maney introduced the slope-deflection method as one of the classical methods of analysis of indeterminate beams and frames. Slope-Deflection Method of Analysis of Indeterminate Structures

Karamba space frame deflection